ODE
\[ \left (x^2-y(x)\right ) y'(x)=4 x y(x) \] ODE Classification
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Change of Variable, new dependent variable
Mathematica ✓
cpu = 0.290493 (sec), leaf count = 232
\[\left \{\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {i \sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}-(1-i)}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {i \sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {\sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {\sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}-(1-i)}\right )\right \}\right \}\]
Maple ✓
cpu = 0.182 (sec), leaf count = 53
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \left (\textit {\_C1} -\sqrt {\textit {\_C1}^{2}-4 x^{2}}\right )}{2}-x^{2}, y \left (x \right ) = \frac {\textit {\_C1} \left (\textit {\_C1} +\sqrt {\textit {\_C1}^{2}-4 x^{2}}\right )}{2}-x^{2}\right ]\] Mathematica raw input
DSolve[(x^2 - y[x])*y'[x] == 4*x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) + (I*Sqrt[2])/Sqrt[-I + x^2*Cosh[(2*C[1])/9] + x^2*Sinh[(2*C[1])/9]]))}, {y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) - (I*Sqrt[2])/Sqrt[-I + x^2*Cosh[(2*C[1])/9] + x^2*Sinh[(2*C[1])/9]]))}, {y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) - Sqrt[2]/Sqrt[I + x^2*Cosh[(2*C[1])/9] + x^2*Sinh[(2*C[1])/9]]))}, {y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) + Sqrt[2]/Sqrt[I + x^2*Cosh[(2*C[1])/9] + x^2*Sinh[(2*C[1])/9]]))}}
Maple raw input
dsolve((x^2-y(x))*diff(y(x),x) = 4*x*y(x), y(x))
Maple raw output
[y(x) = 1/2*_C1*(_C1-(_C1^2-4*x^2)^(1/2))-x^2, y(x) = 1/2*_C1*(_C1+(_C1^2-4*x^2)^(1/2))-x^2]